The possibility of using component analysis for
nominal data is discussed. Particularly, two nominal
scale correlation coefficients are applicable,
namely, Tschuprow’s coefficient and the J index.
The reason is that they are E-correlation coefficients;
that is, they satisfy the requirements of a
scalar product between normalized vectors in a Euclidean
space. Some characteristics of these coefficients
are described. The contingency coefficient
and Cramer’s V are shown not to be applicable in a
component analysis. An example of a truncated
component analysis on artificial nominal data is included
with both the J index and Tschuprow’s coefficient.
Janson, Svante & Vegelius, Jan. (1978). On the applicability of truncated component analysis based on correlation coefficients for nominal scales. Applied Psychological Measurement, 2, 135-145. doi:10.1177/014662167800200113
Janson, Svante; Vegelius, Jan.
On the applicability of truncated component analysis based on correlation coefficients for nominal scales.
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